“Tomography,” as used here, is a general term describing various techniques for imaging one or more cross-sectional “focal plane(s)” through an object. Tomography typically involves forming projections of a region of interest using some type of penetrating radiation, such as x-rays, sound waves, particle beams, or products of radioactive decay, that are then combined with the application of a reconstruction technique. Tomography has been applied in diverse fields to objects ranging in size from microscopic to astronomical. X-ray tomography, for example, is commonly used to inspect solder joints for defects formed during fabrication of printed circuit assemblies.
In “laminography,” also known as “classical tomography,” two or more of the source, object, and detector are moved in a coordinated fashion during exposure to produce an image of the desired plane on the detector. It is also possible to replace mechanical motion with electronic scanning (e.g. of the source or detector). The motion may be in a variety of patterns including, but not limited to, linear, circular, helical, elliptical, or random. In each case, the motion is coordinated so that the image of the focal plane remains stationary and in sharp focus on the detector, while planes above and below the focal plane move and are blurred into the background. Reconstruction takes place in the detector during exposure and consists simply of integration. Laminography can be considered a form of “dynamic tomography” since motion is typically continuous throughout exposure.
Like laminography, tomosynthesis requires coordinated positioning of the source, detector and object. In fact, similar data acquisition geometries may be used in each case. Tomosynsthesis differs from laminography in that projections are acquired with the motion stopped at multiple, fixed points. Reconstruction is then performed by digitally averaging, or otherwise combining, these projections.
Tomosynthesis can be considered a digital approximation to laminography, or a form of “static tomography,” since the source and detector are typically stationary during each projection. However, this dichotomy between dynamic and static tomography is somewhat dated and artificial since numerous hybrid schemes are also possible. Tomosynthesis, which can also be considered a specific form of computed tomography, or “CT,” was first described in D. Grant, “Tomosynthesis: A Three-Dimensional Radiographic Imaging Technique”, IEEE Trans. Biomed. Eng: BME-19: 20-28, (1972), and incorporated by reference here.
In typical laminography, a single, flat focal plane is chosen in advance for imaging during an acquisition cycle. With tomosynthesis, on the other hand, a single set of projections may be used repeatedly to reconstruct images of focal planes at varying heights. This “tomosynthetic reconstruction” is typically accomplished by shifting or translating the projections relative to each other prior to combining.
A common problem for many types of tomography is that the region(s) of interest may not lie in a single, flat plane, and, indeed, may be arranged on one or more arbitrarily complex surfaces. For example, one may wish to image solder joints in a region of a printed circuit board which is warped or the complex articular surface of a biological joint in a medical application. Tomosynthetic reconstruction of tilted, flat planes is generally described in J. Liu, D. Nishimura, and A. Macovski, “Vessel Imaging Using Dual Energy Tomosynthesis”, Med. Phys. 14(6): 950-955 (1987) and in Z. Kolitsi, G. Panayiotakis, V. Anastassopoulos, A. Scodras, and N. Pallikarakis, “A Multiple Projection Method for Digital Tomosynthesis,” Med. Phys. 19(4): 1045-1050 (1992), which are both incorporated by reference here. However, these references do not consider the various problems associated with curved, or otherwise non-flat, focal planes such as warped printed circuit boards.
In some cases the acquisition geometry may be adapted to accomplish this for a particular application. For example, JP52030395 to Shoichi is incorporated by reference here and, according to an English-language abstract, discloses a curved tomography camera for panoramically photographing a specific curved dislocation region in a horizontal patient. The Shoichi drawings appear to illustrate a collimated x-ray source and a rotating detector moving in arcs that are concentric with the human ribcage being imaged. While well-suited for relatively simple shapes which are known in advance, such an approach appears to lack the flexibility to adapt to arbitrarily complex surfaces determined at run time.
With regard to dynamic tomography, U.S. Pat. No. 5,687,209 to Adams (assigned at issuance to Hewlett-Packard Co.) discloses a laminography system with automatic test object warp compensation and is also incorporated by reference here. The Adams laminography system uses two or more linear detectors and one or more collimated X-ray sources. Discrete X-ray images, with different viewing angles, are generated by each detector and then analyzed by a computer to generate Z-axis test object warp compensation parameters based upon the location of a pre-determined feature in a test object found in each image. The discrete X-ray images are then combined using these warp compensation parameters to generate laminographic images of different planes in the object under test.
However, the Adams technique uses features in each of several shadowgraph images to determine a two-dimensional shift distance for the entire image in the corresponding shadowgraph. The technique can therefore produce distorted reconstructions for a variety of reasons discussed in more detail below.